Re: The width, length, and diagonal of a rectangle could [#permalink]
11 Jan 2019, 09:44

1

This post receivedKUDOS

Expert's post

GreenlightTestPrep wrote:

The width, length, and diagonal of a rectangle could be represented by which of the following groups of numbers?

I. 2, 3, \(\sqrt{13}\)II. \(\sqrt{10}\), 4, 6III. 3, 10, 11

A. I only B. I and II onlyC. I and III onlyD. II and III onlyE. I, II, and III

NOTE: The width, length, and diagonal create a RIGHT TRIANGLE, with the diagonal as the hypotenuse. For these to be valid lengths, the Pythagorean Theorem must apply. That is, it MUST be the case that width² + length² = diagonal²

Let's check the 3 sets of values BEGINNING WITH III

III. Does 3² + 10² = 11²? NO. This means that 3, 10, 11 CANNOT represent the width, length, and diagonal of a rectangle.This means we can ELIMINATE C, D and E

II. Does (√10)² + 4² = 6²? NO. This means that √10, 4, 6 CANNOT represent the width, length, and diagonal of a rectangle.This means we can ELIMINATE B